Abstract

Uncertainty principle between two observable quantities in quantum mechanics is the reason of their non-simultaneous measurability. Uncertainty principle has long been investigated and developed in a variety of representations. However, in many textbooks (see Modern Quantum Mechanics, J.J. Sakurai) the anti-commutation part of uncertainty principle is eliminated due to have more stronger non-equality in it.  By investigating the uncertainty principle in phase space quantum mechanics in Wigner representation for the squeezed number states we find that this anti-commutation  part is in general non-negligible, at least for squeezed number states.